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;; Example 2.56
(define (=number? exp num)
(and (number? exp) (= exp num)))
(define (variable? e)
(symbol? e))
(define (same-variable v1 v2)
(and (variable? v1) (variable? v2) (eq? v1 v2)))
(define (sum? e)
(and (pair? e) (eq? (car e) '+)))
(define (addend e)
(cadr e))
(define (augend e)
(caddr e))
(define (make-sum a1 a2)
(cond ((=number? a1 0) a2)
((=number? a2 0) a1)
((and (number? a1) (number? a2)) (+ a1 a2))
(else (list '+ a1 a2))))
(define (product? e)
(and (pair? e) (eq? (car e) '*)))
(define (multiplier e)
(cadr e))
(define (multiplicand e)
(caddr e))
(define (exponentiation? e)
(and (pair? e) (eq? (car e) '**)))
(define (base e)
(cadr e))
(define (exponent e)
(caddr e))
(define (make-exponentiation b e)
(cond ((=number? b 0) 0)
((=number? e 1) b)
((=number? e 0) 1)
((and (number? b) (number? e)) (expt b e))
(else (list '** b e))))
(define (make-product m1 m2)
(cond ((or (=number? m1 0) (=number? m2 0)) 0)
((=number? m1 1) m2)
((=number? m2 1) m1)
((and (number? m1) (number? m2)) (* m1 m2))
(else (list '* m1 m2))))
;; Derivative
(define (deriv exp var)
(cond ((number? exp) 0)
((variable? exp)
(if (same-variable exp var) 1 0))
((sum? exp)
(make-sum (deriv (addend exp) var)
(deriv (augend exp) var)))
((product? exp)
(make-sum (make-product (multiplier exp)
(deriv (multiplicand exp) var))
(make-product (deriv (multiplier exp) var)
(multiplicand exp))))
((exponentiation? exp)
(make-product (exponent exp)
(make-product (make-exponentiation (base exp)
(make-sum (exponent exp) -1))
(deriv (base exp) var))))
(else
(error "XYNTA " exp))))
(deriv '(** x 2) 'x)
(deriv '(** x (* 2 x)) 'x)
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